Do you suppose that a person who’s spent about 2.5 years training themselves to withstand/ignore pain by say experiencing 4th degree burns over his entire body, would be able to throw one punch before collapsing after being stabbed in the lung?

Okay, so, two problems up front. The first being
that: Fourth degree burns aren’t painful. There may be some exceptions, but the
nerve endings are cooked, so nothing remains to transmit to the brain that this
should hurt, or even that the injury is occurring. The second is that: Fourth
degree burns don’t heal. As I mentioned a second ago, fourth degree burns are
where the tissue has been cooked, the meat itself is dead at this point.

Without immediate and extensive medical treatment,
fourth degree burns are life threatening injuries. These are where the burn
gets into the deep tissue, destroying muscles, ligaments, tendons, and any nerves
unfortunate enough to be affected. Usually, fourth degree burns penetrate to
the bone, so if it’s a limb, that’s not coming back.

Also, note the word I used above, “cooked.” That’s a
pretty good description of the kind of damage we’re talking about here. It’s
not something your character can walk away from.

Second, following up on what I said the other day
about injuries, pain, and adrenaline. If you missed it, the very short version
is that adrenaline actually impairs your ability to feel pain (to a degree), so
if you’re in combat and take a bullet, or get stabbed.

To an extent, none of this matters, a character can
keep fighting with a collapsed lung, but their ability to breathe will be
impaired. Lungs function operate based on controlled air pressure, so when they’re
punctured, they tend to deflate, halving the victim’s ability to breathe. They’d
suffer everything that comes along with hypoxia: Shortness of breath,
lightheaded, easily fatigued, and confusion, (I assume the confusion would take
a few minutes, but I’m not 100% certain). A collapsed lung can also cause the
victim to go into shock.

There is a point to teaching people to manage pain,
and the methods for that, ranging from extremely intensive exercise to some
varieties of very controlled physical abuse, but setting someone on fire does
not qualify as either, and fourth degree burns are something that will halt
your character’s training, it won’t toughen them up, but will turn them into a slab
of meat, cooked well done.

The issue is, a lot of writers take the idea of
things like extreme training, and push it way past any reasonable stopping
point. Fourth degree burns is up there with shooting a character to teach them
to control pain. Unless they have superpowers, it will transition from the
kinds of pain someone can learn from and into actually killing the student. A
character might get to the point where they’re being struck with a staff and
taking the blows without injury through proper muscle control, but you’re not
going to run them through with a sword, or set them on fire. That doesn’t teach
anything, and will seriously injure the student.

Following on that, the purpose of striking a student
is to teach them to take blows without being injured. They’re learning to tense
the muscles so the impact doesn’t cause harm.

Exercise is where you learn to tune out pain.
Someone used to sprinting on wet sand will be far better suited to powering
through pain than someone who was repeatedly set on fire by a sadistic
instructor. Also, I called this extreme exercise earlier, but this stuff is
still pretty tame. It will include things like asking the students to exercise
in unpleasant circumstances, not ones that pose an actual treat to them.

So, in short, yes, they can keep fighting, though it’s
not going to be as simple as they fall over, they’ll slow down, start losing
track of what’s going on, probably get far more seriously injured because they’re
still trying to participate against unimpaired foes, and then collapse.